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Computing equilibrium in network utility-sharing and discrete election games

Author

Listed:
  • Rahul Swamy

    (University of Illinois at Urbana-Champaign)

  • Timothy Murray

    (University of Illinois at Urbana-Champaign)

Abstract

This paper studies the computation of pure Nash equilibrium (PNE) in network utility-sharing and discretized Hotelling–Downs games, and the interplay between these classes of games. First, we introduce and study a variant of network utility-sharing games with additional player-specific non-shareable costs (NUSG+), which is shown to possess a PNE. We extend polynomial-time PNE computation results to a class of graphs that generalizes series-parallel graphs when the non-shareable costs are player-independent. Second, a spatial election game is introduced with a discretized utility function. The complexity of this game is shown to be in Polynomial Local Search, and a polynomial-time PNE computation is derived for certain settings. Third, a spatio-temporal election game model is presented based on an NUSG+ when voter opinions form natural discrete clusters. This model captures several variants of the classic Hotelling–Downs election model, including ones with limited attraction, ability of candidates to enter, change stance positions and exit any time during the campaign or abstain from the race, the restriction on candidates to access certain stance positions, and the operational costs of running a campaign. Finally, we provide a polynomial-time PNE computation for an election game when stance changes are restricted.

Suggested Citation

  • Rahul Swamy & Timothy Murray, 2022. "Computing equilibrium in network utility-sharing and discrete election games," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 2056-2084, October.
  • Handle: RePEc:spr:jcomop:v:44:y:2022:i:3:d:10.1007_s10878-020-00554-8
    DOI: 10.1007/s10878-020-00554-8
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    References listed on IDEAS

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    1. Osborne Martin J., 1993. "Candidate Positioning and Entry in a Political Competition," Games and Economic Behavior, Elsevier, vol. 5(1), pages 133-151, January.
    2. Richard D. McKelvey & Richard E. Wendell, 1976. "Voting Equilibria in Multidimensional Choice Spaces," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 144-158, May.
    3. H. A. Eiselt & Gilbert Laporte & Jacques-François Thisse, 1993. "Competitive Location Models: A Framework and Bibliography," Transportation Science, INFORMS, vol. 27(1), pages 44-54, February.
    4. Marcin Dziubiński & Jaideep Roy, 2013. "Hotelling–Downs Competition with Free Entry When Voters Have an Option to Contest," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(4), pages 620-653, August.
    5. Duggan, John & Fey, Mark, 2005. "Electoral competition with policy-motivated candidates," Games and Economic Behavior, Elsevier, vol. 51(2), pages 490-522, May.
    6. Brusco, Sandro & Dziubiński, Marcin & Roy, Jaideep, 2012. "The Hotelling–Downs model with runoff voting," Games and Economic Behavior, Elsevier, vol. 74(2), pages 447-469.
    7. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    8. H. A. Eiselt & Gilbert Laporte, 1993. "The Existence of Equilibria in the 3-Facility Hotelling Model in a Tree," Transportation Science, INFORMS, vol. 27(1), pages 39-43, February.
    9. Sengupta, Abhijit & Sengupta, Kunal, 2008. "A Hotelling-Downs model of electoral competition with the option to quit," Games and Economic Behavior, Elsevier, vol. 62(2), pages 661-674, March.
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